FORTUNE — Look around, anywhere really, and you’ll see the upshot of somebody trying to sell you something. Big companies try to cover all the bases — everything from billboards in Times Square to pithy tweets — to hit the algorithm that will put their brand on your brain.

It’s a rat race, vying for all that mental space, especially when customers are growing more skeptical. The result of the ad deluge is that, for some companies, the best strategy is to opt out.

Take Signature Bank (SBNY), one of the companies on Fortune’s 2011 fastest-growing companies list. Without any advertising, it has grown significantly, from about $50 million when it launched in 2001 to $13.1 billion in assets this year. This past quarter, the bank had a net income of $36.6 million, up by 64% from the previous year.

In many ways, the bank is especially suited for the no-ad tactic: it targets New York-based small businesses, and offers clients one point of contact for all banking services. A client can call Signature to set up a line of credit for a business and then ask about financing a house in the Hamptons in the next breath. These aren’t customers who chose their bank based off of ads at a Yankee’s game, says CEO Joe DePaolo. Instead, they rely on recommendations from friends and associates.

That’s actually the most effective way to reel people in, says Rajkumar Venkatesan, a professor of business administration at the University of Virginia’s Darden School of Business. Customers acquired through word of mouth are more profitable for the company, over time, than customers who join through other types of advertising, he says. The social bond is strong glue.

That’s especially true for people like Signature’s high-end New York clients — the lack of advertising plays into the company’s aura of elitism. Especially regarding financial decisions, Venkatesan says, “People want access to something that everyone doesn’t have so they can get better returns.” Opting out amid a glut of big bank advertisements gives Signature a secret, club-like edge.

“Think about how many advertisements for financial services you see in a typical week, especially in Manhattan. Crazy amounts of them, and all of them are about being ‘reputable,’ and ‘serious,’” says Gavan Fitzsimons, a professor of marketing and psychology at Duke University. Why not just be reputable and serious and let your business spread organically?

More companies will start to do this, Fitzsimons predicts, even though businesses that back out of the ad race risk ceding control of the conversation. Still, people’s brains are so saturated with advertisements that more exposure isn’t necessarily better. “The bottom line is, now a consumer sees an ad and their defensive mechanisms automatically come up,” says Fitzsimons.

In fact, according to Fitzsimons’ research, the best result that an advertiser can hope for is to nudge us in the direction we were already going — reaffirming a slightly positive association with a brand that we already liked.

Certainly, many marketers are chasing that positive nudge, which can be a powerful tool. At the more engaged end of the advertising spectrum, marketers often vie for the Holy Grail that is viral marketing via social media. The formula is unpredictable, but sometimes, advertisers hit a sweet-spot and make an ad or start a campaign that we like so much we spread it ourselves by sending links to friends or tweeting or posting it to Facebook.

Proctor & Gamble (PG) struck gold with this last year, when they created an interactive social media campaign for Old Spice around actor Isaiah Mustafa. The method certainly has its merits, says Venkatesan, especially since many social media ad campaigns require very little capital. Companies can afford to be agile, he says, and try different options. When one sticks, they encourage its rapid growth, already in progress.

But at the other end of the marketing spectrum, the oldest branding strategy of all is making a comeback: deliver a quality product or service and sit back and wait for the customers to come to you.

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